Consider the following linear program: Min 8X + 12Y s.t. 1X + 3y = 9 2X+ 2Y≥10 6X2Y 18 X, Y≥0 b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number. The same extreme point remains optimal ✓ Y Optimal solution c. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number. A new extreme point becomes optimal ✓ X Y Optimal solution d. The computer solution for the linear program in part (a) provides the following objective coefficient range information: Variable X Y Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem? The objective coefficient range for variable X is to . Since the change in part (b) is in this range, we know that the optimal solution will not change. The objective coefficient range for Y is from not in this range. to so the optimal solution will change in part (c) because the new objective coefficient is